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Question 1028203: jenny does ironing for a local dry cleaner she is paid 150 per month plus .25 per shirt and 1.50per pair of slacks. last month she ironed 300 pieces and made 325 how many shirts did she iron and how many slacks.
PLEASE HELP ME AS SOON AS POSSIBLE THANK YOU
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of shirts she ironed
y = number of slacks she ironed
she gets paid 150 a month plus .25 for each shirt + 1.5 for each pair of slacks.
her revenue for the month is therefore equal to 150 + .25 * x + 1.5 * y
last month she ironed 300 piece of clothing.
this means x + y = 300
last month she earned 325
her revenue for the month is 325 dollars.
the revenue equation is r = 150 + .25 * x + 1.5 * y
the revenue equation becomes 325 = 150 + .25 * x + 1.5 * y
you know that x + y = 300
solve for y to get y = 300 - x
in the equation of 325 = 150 + .25 * x + 1.5 * y, replace y with 300 - x to get:
325 = 150 + .25 * x + 1.5 * (300 - x)
subtract 150 from both sides of this equation to get:
175 = .25 * x + 1.5 * (300 - x)
simplify by expanding the expression on the right side of the equation to get:
175 = .25 * x + 1.5 * 300 - 1.5 * x
simplify further and combine like terms to get:
175 = -1.25 * x + 450
subtract 175 from both sides of the equation and add 1.25 * x to both sides of the equation to get:
1.25 * x = 450 - 175
combine like terms to get 1.25 * x = 275
divide both sides of the equation by 1.25 to get x = 275 / 1.25 = 220.
since x + y = 300, then y = 300 - 220 = 80.
you get x = 220 and y = 80
this means she ironed 220 shirts and 80 pairs of slacks.
the revenue equation becomes 325 = 150 + .25 * 220 + 1.5 * 80
simplify to get 325 = 150 + 55 + 120
combine like terms to get 325 = 325
this confirms the solution is correct.
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